XPM Prime Explorer symbol
XPMPrime Explorer

Block #175,358

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2013, 6:02:26 AM Β· Difficulty 9.8636 Β· 6,641,621 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
b22f60dbeb8f327fe24d993046bc2e2c3be52e36bdc85ec5d326d9e35bcb79d3
View on Chainz β†—

Height

#175,358

Difficulty

9.863630

Transactions

1

Size

199 B

Version

2

Bits

09dd16dd

Nonce

32,180

Timestamp

9/22/2013, 6:02:26 AM

Confirmations

6,641,621

Mined by

⛏️ P2SHAM1A9CZLPnH51axL7hPRTWjkm6as4Lpogj

Merkle Root

c870db305036894a29022db7bf41eaf41228c9a4e819f85101f848d63131eb8e
Transactions (1)
Coinbasec870db30503689…f848d63131eb8e
1 in β†’ 1 out10.2600 XPM109 B
AM1A9CZL…as4Lpogj
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.305 Γ— 10⁹⁴(95-digit number)
23053251152310025397…20120140032150393601
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.305 Γ— 10⁹⁴(95-digit number)
23053251152310025397…20120140032150393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.610 Γ— 10⁹⁴(95-digit number)
46106502304620050795…40240280064300787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.221 Γ— 10⁹⁴(95-digit number)
92213004609240101590…80480560128601574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.844 Γ— 10⁹⁡(96-digit number)
18442600921848020318…60961120257203148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.688 Γ— 10⁹⁡(96-digit number)
36885201843696040636…21922240514406297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.377 Γ— 10⁹⁡(96-digit number)
73770403687392081272…43844481028812595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.475 Γ— 10⁹⁢(97-digit number)
14754080737478416254…87688962057625190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.950 Γ— 10⁹⁢(97-digit number)
29508161474956832508…75377924115250380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.901 Γ— 10⁹⁢(97-digit number)
59016322949913665017…50755848230500761601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,779,870 XPMΒ·at block #6,816,978 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy